OEIn this question you are asked to compare the area of rectangle P with that of rectangle Q. Since the information given is the relative size of the length and width of rectangles P and Q with respect to those of rectangle P, you should try to evaluate the relative areas using rectangle P's dimensions as the starting point.
If you assign x to the length of rectangle P, and y to its width, you get an area for rectangle P of xy. Because the length and width of rectangle P are 30 percent less and 20 percent greater, respectively than those of rectangle P, then the length and
width of rectangle P equal (1 - 0.3)* = o.yx and (l + o.2)y = i.2y. Thus, the area of rectangle P is (0.7*) (i.2y) = 0.84xy.
Similarly, the length and width of rectangle Q are 40 percent greater and 40 percent less, respectively, than those of rectangle P, so the length and width of rectangle Q equal (1 + 0.4)x = 1.4X and (1 - 0.4)y = 0.6y. Thus, the area of rectangle Q is (i.4x)(0.6y) = 0.84xy.
Thus, rectangles P and Q have equal area. Therefore, the two quantities are equal.
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